No, unless the laws change, you cannot own an MP5. It was banned from import for civilians by the GCA68, which prohibited the import of foreign made machine guns (Even though it had not yet been invented yet). The GCA86 banned the manufacturer of US made machine guns for civilians, but HK never made the MP5 in the US, so there are none here for civilians.

Those that claim to have an MP5 really have an HK-94 that was legally converted, or an SP-89 that was legally converted with pre-GCA86 parts. Some with these weapons even go so far as to have the weapon stamped "MP5". If the HKPRO BBS ever comes back to life, you can view the archives for more info.